Strictly speaking, if you want to study CS and have a lot of freedom, look at programs outside of colleges of engineering. Employers (and even grad schools) won’t distinguish between BA vs. BS, because the main difference is that the BS has more required classes in your major, but you can take as many with a BA, you simply get to choose them. Most colleges will require you to have about 1/3 of your classes in general education classes to make sure you’re broadly educated. 1/3 will be your major. The 1/3 left can be free electives, complementary classes, core classes, it all depends on the college.
Look into Harvey Mudd, by the way, since it has both the strong science component and the Liberal Arts component you’re seeking. However you need to be the tippy-top student at your school, with scores in the 750-800 bracket, and calculus is a pre-requisite (the only school in the US with CalTech that requires it in HS, and where most applicants have way more than that).